In this work, we study an abstract boundary-value problem generated by an evolution equation and a non-local boundary condition. We prove the existence and uniqueness of the strong generalized solution and its continuity to respect to the parameters. The proofs are obtained via a priori estimates in non classical functional spaces and on the density of the range of the operator generated by the...

Using the framework introduced by Rowley and Colonius [14] we construct a discretely non-reflecting boundary condition for the one-way wave equation spatially discretized with an explicit fourth order centered difference scheme. The boundary condition, which can be extended to arbitrary order accuracy, is shown to be GKSstable. We continue by deriving discretely non-reflecting boundary conditio...

We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an...

We consider the solution of the Helmholtz equation−∆u(x)−n(x)ωu(x) = f(x), x = (x, y), in a domain Ω which is infinite in x and bounded in y. We assume that f(x) is supported in Ω := {x ∈ Ω |a− < x < a} and that n(x) is x-periodic in Ω\Ω. We show how to obtain exact boundary conditions on the vertical segments, Γ− := {x ∈ Ω |x = a−} and Γ := {x ∈ Ω |x = a}, that will enable us to find the solut...

Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type, subject to non-local boundary conditions; by contrast, its adjoint is the sum of a Laplacian and of a singular Green operator, subject to local boundary condition...

A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...

Numerical solutions for open-region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions (RBCs) for general boundary shapes have been proposed during the past decade. Many are generalizations of the Bayliss-Turkel RBC for circular truncation boundaries. This paper reviews several two-d...